Posted on 04/06/2010 7:07:19 AM PDT by truthfinder9
Forget quantum, forget light, your argument is getting obtuse. The point is whether mathematic proof is proof of truth and facts.
If the Pythagorean theorem is proved mathematically, is it therefore proven “true” - a “fact”? If it is mathematically proven false, is it therefore “false”. If it is mathematically proven unprovable, is it therefore a fact that it is “unprovable.”
So does Ptolemaic navigational system
It works precisely because it reflects the real world
Working models do not represent reality. Ptolemaic navgiational system being a perfect example.
I AM talking about proof. Are you off trying to deny mathematical proof now?
Facts have to be provable against reality. Otherwise they are not facts.
You do believe 2+2=4, right?
No I don't believe it, I KNOW it. No faith required here.
If something is unprovable (in a given working model) it is simply unprovable. It is not "proven" unprovable.
Since we are on semantics, if it ismathematically proven false then it is mathematically false. That doesn't mean it is necessarily false as regards the real world.
What do you think mathematic proofs are about?
That doesn't mean it is necessarily false as regards the real world.
Mathematics is the real world of quantifiable facts.
No, one can prove that a statement or fact is unprovable. I gave you an example.
These are real world quantities and real world geometries.
If you cannot accept mathematic proof, then your problems are moreso with logical proofs - and any argument you make fails by your own test.
Boolean algebra, the math of logic, would also fail your proof test.
There is no basis for any proof in your system.
You do not recognize the most precise objective facts and proofs capable by humans.
And do you know that if a store has 224 dozen eggs, they have 2,688 eggs? How?
False on all three accounts.
I never said that.
Yet, you would not know that the Pythagorean Theorem is truth without the mathematic proof
Mathematical proof are theorems. Theorems are not facts. They are true within the mathematical working model based on axiomatic assumptions in all cases. They do not describe reality.
If reality happened to correspond to the axiomatic assumptions involved in a theorem, then the theorem will describe the factual reality, but only under those conditions (in Pythagorean case a natural object would have to be triangular and one of its angles would have to to be an exact [to the nth decimal], perfect 90 degrees).
Of course there are no true 90 degree angles in nature; they "exist" as conditional axiomatic assumptions in Euclidean geometry, and therefore the theorem does not correspond to reality. So the Pythagorean Theorem does not apply to the real world, describe reality, or 'prove' it. It's pure theory.
These are real world quantities and real world geometries
Geometric shapes are perfect assumptions. Classical geometry is an idealized system which does not quantitatively or otherwise correspond to the real world, and is therefore only an approximation of it; it is an approximate description of the world.
The system is true only in its idealized form, but the real world is not ideal.
If you cannot accept mathematic proof, then your problems are moreso with logical proofs - and any argument you make fails by your own test
Logical proofs also operate in an ideal environment of assumed axiomatic "truths." That's why so many believers find logic dear and near when it comes to "proving" God logically. Such proofs are theorems under assumed conditions, and have no bearing on the real world, nor can they be verified in the real world for that reason.
My arguments are not logical but empirical. Empirical proof is the only proof. All else is theoretcial. An optical engineer can tell you that his system (on paper) will be diffraction-limited to the edge of the image field, but the final wavefront that reaches the focus depends on much more than theoretical design.
My tagline is pure empiricism. The world is the way it is even if it is not logical. We can't argue with the world logically.
By knowing that a "dozen" represents a set of 12, and then either by adding them or by taking the shortcut—multiplying them! Multiplication is just fancy short-hand addition. This particular problem has a real-world counterpart and can actually be proven as a natural fact.
Sure there is. But it does not necessarily describe, let alone, "prove" the real world.
You do not recognize the most precise objective facts and proofs capable by humans
I do and I also recognize that they must be understood in proper context and scope as theoretical.
If they are to be considered factual, they must correspond to the observable, detectable world.
Observable, but not provable, at least not mathematically. It used to bother me that all our knowledge and I mean all human knowledge, is an approximation to truth and fact. We can observation and interpret and approximate with remarkable accuracy but every aspect of our live is lived with some gap of the undefined or unknown. This gap is closed with what theologians call faith and scientists call theory. It's entertaining to contemplate while fishing or smoking a nice cigar.
By knowing that a "dozen" represents a set of 12, and then either by adding them or by taking the shortcut—multiplying them! Multiplication is just fancy short-hand addition.
How do you know in this case? Did you get 2,688 eggs.
This particular problem has a real-world counterpart and can actually be proven as a natural fact.
You haven't proven that empirically.
You denied a "real-world" counterpart to polynomial equations I referenced earlier. On what basis? Algebra?
Do you multiply 12 times 224 or 224 times 12? Does it matter? How do you know? Empirically.
You have thoroughly dug yourself into a hole.
If you have a measuring device capable of measuring distance and angles to a significant degree of "real world" accuracy, will the Pythagorean Theorem apply to the real world, describe reality to the same degree of accuracy as you are capable of? Using these measurements and mathematics can you prove it in the real world? Why?
Indeterminable, not unprovable. No one doubts pi.
It used to bother me that all our knowledge and I mean all human knowledge, is an approximation to truth and fact
Why?
We can observation and interpret and approximate with remarkable accuracy but every aspect of our live is lived with some gap of the undefined or unknown
I think that is a sweeping generalization. There is no gap in our knowledge that the earth is round, that the sun doesn't go around us but we around the sun, etc. There are a lot of things we know for sure. The "gap" has to do with the degree to which we know things.
Most humans seme to have difficulty accepting that perhaps they are not capable of knowing everything; some even believe they are entitled to knowing everything.
This gap is closed with what theologians call faith and scientists call theory
Not really closed. Theory and faith are very much open-ended, by definition; but some mistakenly take them as close-ended.
It's entertaining to contemplate while fishing or smoking a nice cigar.
All of which is the benefits of the artificial world we created that makes us comfortable enough to engage in such trivia. We live in a bubble called the civilized world, which has no bearing to the world around us.
No, but I can buy them. I can also use 2,688 pebbles instead of eggs, and arrange them in groups of 12 each, then count the number of groups.
Luckily we invented shortcuts to physical counting, but if anyone doubts, the longer method is always available.
You haven't proven that empirically
I just have. But you are more than welcome to buy 244 dozen eggs and start counting. You don't have to take my word for it. You don't have to take my word for gravity either. A 20th flood seems like good starting point...to think about it on the way down. :)
You denied a "real-world" counterpart to polynomial equations I referenced earlier
Where is the real world application to those polynomial equations. Polynomials are used in optical design all the time, but their real-world counterpart can be carried only to two or three terms in a string of theoretically infinite number of terms. That is hardly a real-world counterpart, but an ideal real world appoximation.
An ideal is not a real-world counterpart but a fantasy. The perfect celestial spheres concept went out with Galileo. Of course, the Church was trying to tell him that the Moon was really unblemished and perfect, and that the devil (!) was distorting his view to make him think celestial bodies were imperfect. Why let reality get in the way of a perfectly concocted fantasy, right?
Do you multiply 12 times 224 or 224 times 12? Does it matter? How do you know? Empirically.
Sometimes I think sophism is a disease.
Ha!
If you have a measuring device capable of measuring distance and angles to a significant degree of "real world" accuracy will the Pythagorean Theorem apply to the real world, describe reality to the same degree of accuracy as you are capable of?
There is no such thing as a perfect right angle triangle in nature. The Pythagorean Theorem describes the real world in ideal terms. Spheres approximate celestial bodies such as the Moon, Mars, etc. but these are not perfect spheres, so all Euclidean geometry is a schematic approximation of the real world and consequently the ratios obtained through it are approximations as well.
The Pythagorean Theorem is true only in triangles that have a perfect 90 degree angle. In all other cases it is an appxorimation. But where would you draw the line? At 89, 88, 87, 82.567 degrees for an "acceptable" approximation? The Theorem is theoretically true only for theoretically perfect triangles.
Look, a perfect parabolic mirror, in theory, will focus all the light coming from a distance point source to a perfect point. But, there is no such thing as a perfect parabolic mirror and the nature of light makes it impossible to concentrate all the energy into a point, even if the mathematics say it can. Nature trumps math every time.
Using these measurements and mathematics can you prove it in the real world? Why?
Prove what? That the hypotenuse value squared is exactly the sum of the squares of the sides? No.
Yes. To whatever degree of accuracy you use.
No.
Call Scientific American, the Pythagorean Theorem has been revoked.
Just when I thought you couldn't dig any deeper...
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